$($b$)$ The Analytic Hierarchy Process $($AHP$)$ may be used where pairwise

comparisons of objectives and opportunities are available. The general

promotions committee is considering two lecturers, A and $B,$ for

promotion. The committee bases its decision on three criteria;

Teaching, Research and Service. The comparisons of the criteria yields

the following matrix;

Comparison of the lecturers yields the following matrices;

Teaching

A B

A $12$

B $\frac{1}{2},1$

Research

A B

A $\frac{11}{4}$

B $4,1$

Service

A B

A $12$

B $\frac{1}{2},1$

Using these comparisons, apply the AHP and answer;

$($i$)$ What percentage weighting is the committee placing on each of

Teaching, Research and Service in evaluating each candidate?

$[5$ marks$]$

$($ii$)$ Which candidate is more favourable? Explain.

$[4$ marks$]$

$($iii$)$ Discuss why for large numbers of choices pairwise comparisons

may be mutually inconsistent.

$[4$ marks$]$